My background: I used to live on a nuclear powered cruise ship. The amenities weren’t much to write home about, the ports we visited were definitely second rate, and food, frankly, sucked.
It was run by the US Navy, and it’s name was the USS Virginia.
I was one of the radiological control technicians on board and for my last two years aboard I was the man in charge of giving the all-hands radcon training to all newly reporting personnel, and to everyone who wasn’t nuclear trained at least once a year. Based on what I taught I can assure you: a cruise ship wouldn’t need much training of it’s passengers for the basics of the safety concerns they have to be aware of aboard a nuclear powered vessel. Certainly it could easily be combined with the training they’re supposed to get for lifeboat and fire drills. Unfortunately, a cursory look at historical cruise ship disasters going all the way back to the SS Morrow Castle make it clear that the majority of cruise lines don’t want to annoy their passengers with this training if they can possible avoid it.
More to the point, using a Pressurized Water Reactor (The kind used by the US and Russian navies) requires a very manpower intensive crew. As a measuring stick, the Virginia class cruisers and the Ticonderoga class cruisers are very similar ships, with similar missions, displacement, and weaponry. A Ticonderoga class cruiser has a crew of approximately 400; while I was aboard Virginia we rarely had under 600. The main difference in the crew sizes was simply the engineering plants. Some of it was, yes, a larger engineering crew meant that there was a need for additional cooks, and other supporting sailors; another factor was that while we were heavier than a Ticonderoga class ship, we had more space than they did, too - so we had goodies they didn’t have. But the basic difference was the manpower requirements for the engineering plants. Cruise ships want to keep their overhead down as much as possible. If they can get adequate efficiency by using large diesel engines, which can be monitored by one or two watchstanders, why pay for 13 or 15 watchstanders instead? That’s one reason modern cruise ships are diesel powered, not oil or coal fired steam plants like in the heyday of the cruise ship.
Another reason going to overhead, is that steam plants are very maintenance instensive. Corrosion rates are controlled by three things: The reactants available, the presense or absense of liquid water, and temperature. Steam plants are hot, and use steam, so there’s a lot of water running through the piping. Let any contaminants get into that water and you can have metal getting eaten through faster than you may imagine. Chloride ions, very common in seawater, are particularly damaging. All this means that a steam plant needs relatively frequent maintenance, and replacement of parts. The diesel plants being used, don’t have this problem. They still wear out, but no where near as quickly.
Next is the very real problem with the public perception of the safety or lack of it for nuclear power. Frankly, I’d rather live next to a nuclear power plant than next to an oil refinery. But not many share my prejudices.
It would be a hard sell, and even then it would severely limit where you could go - the fact that the ship in question would be civilian might open up some ports currently closed to nuclear warships, but I wouldn’t want to count on that.
Finally, nuclear power has a couple of long term difficulties. First off neutron fluxes do bad things to metals. Over a period of time they make the metal crystals more brittle, and that gets to be a real hassle. And puts an absolute upper limit on the lifetime for one’s plant. Secondly is the whole disposal issue for reactor waste. I understand the political decision to not reprocess spent fuel, but don’t completely agree with it.
Now, none of these problems are what I’d consider insurmountable - going to a pebblebed reactor, using helium gas as the transfer fluid - would reduce both manpower and maintenance costs. The problems are just that at the moment, no one (that I know of) has built a pebble bed reactor, in spite of the many good things to be said about them. But why do all that, when diesel is going to be easier to sell to the customers anyways? And diesel techs are cheaper than rad sponges.